Are you sure the William Braun listed as a messenger at the arsenal 1860 was your ancestor? He was 29 and his oldest child born about 1856, when your ancestor would have been only 13.

The Mo Archives site has seven different listings for Civil War men named William Braun:

http://www.sos.mo.gov/archives/soldiers/results.asp?txtName=braun,%20william&selConflict=Civil%20War&txtUnit=&rbBranch=

The listing for Corp. William Brown of 4th Regt Cavalry, age 30, matches the one in 1860 census.

The listing for Pvt. William Brown of 4th Regt Mo Vols (3 Mos) age 26 is also too old.

Perhaps your family legend is correct and he was the one who served in Co I, 4th Regt EMM 1864 (age not listed but your ancestor would have then been 21)